Question

Describe how to prepare \(1.00 \mathrm{~L}\) of a \(0.646 \mathrm{M} \mathrm{HCl}\) solution, starting with a \(2.00 \mathrm{M} \mathrm{HCl}\) solution.

Short answer

Use 0.323 L of 2.00 M HCl and dilute to 1.00 L with water.

Step-by-step solution

Identify the Formula

To dilute a solution, you can use the dilution formula: \( M_1V_1 = M_2V_2 \). Here, \( M_1 \) is the concentration of the stock solution, \( V_1 \) is the volume of the stock solution you need, \( M_2 \) is the concentration of the final solution, and \( V_2 \) is the volume of the final solution.

Substitute Known Values into the Formula

Given that \( M_1 = 2.00 \, \mathrm{M} \), \( M_2 = 0.646 \, \mathrm{M} \), and \( V_2 = 1.00 \, \mathrm{L} \), substitute these values into the formula: \[ 2.00 \, \mathrm{M} \times V_1 = 0.646 \, \mathrm{M} \times 1.00 \, \mathrm{L} \].

Solve for \(V_1\)

Rearrange the equation to solve for \( V_1 \): \[ V_1 = \frac{0.646 \, \mathrm{M} \times 1.00 \, \mathrm{L}}{2.00 \, \mathrm{M}} \]. Calculate \( V_1 \) to find the volume of stock solution needed: \[ V_1 = 0.323 \, \mathrm{L} \].

Describe the Preparation Process

Measure out \( 0.323 \, \mathrm{L} \) (or \( 323 \, \mathrm{mL} \)) of the \( 2.00 \, \mathrm{M} \) \( \mathrm{HCl} \) solution using a volumetric pipette or a graduated cylinder. Pour this into a \( 1.00 \, \mathrm{L} \) volumetric flask. Add deionized water to the flask until the total volume reaches \( 1.00 \, \mathrm{L} \). Mix thoroughly to ensure the solution is uniform.

Key concepts

Molarity

Molarity is a crucial concept in chemistry for understanding the concentration of solutions. It is defined as the number of moles of a solute divided by the liters of solution. The formula for molarity is \( M = \frac{n}{V} \), where \( n \) is the amount of solute in moles, and \( V \) is the volume of the solution in liters. Molarity gives us a way to quantitatively describe how concentrated or diluted a solution is, which is particularly important for reactions that occur in solutions, as it affects reaction rates and product formation. When preparing solutions for experiments, knowing the molarity helps in predicting how substances will interact on a molecular level, ensuring precise results. This makes molarity a fundamental topic in dilution and concentration calculations.

Volumetric Flask

A volumetric flask is an essential piece of laboratory glassware. It is specifically designed for preparing precise chemical solutions. The flask has a flat bottom and a narrow neck, with a marked line that denotes a precise volume. Using a volumetric flask ensures accurate measurement of liquids because the narrow neck allows for a clear demarcation of volume. This precision is crucial when preparing solutions with specific molarity because any deviation can affect the concentration. For instance, when diluting a stock solution to a specific volume, as shown in the exercise, a volumetric flask helps ensure the final solution is prepared accurately. With the ability to measure exact volumes, it reduces uncertainty in the concentration calculations.

Hydrochloric Acid Preparation

Preparing hydrochloric acid solutions involves careful measurement and dilution to achieve the desired concentration. In the example from the exercise, we start with a concentrated \( 2.00 \mathrm{M} \) HCl solution and aim to dilute it to \( 0.646 \mathrm{M} \).The process begins with calculating the volume of the concentrated solution required, using the dilution formula. Then, this measured volume is transferred to a volumetric flask. The careful addition of deionized water dilutes the HCl to the target concentration.Safety is a key concern when working with HCl due to its highly corrosive nature. It is important to handle it with care, using appropriate personal protective equipment like gloves and goggles. Proper lab procedures also include using fume hoods to avoid inhalation of fumes.

Dilution Formula

The dilution formula \( M_1V_1 = M_2V_2 \) is instrumental in solving problems involving changing the concentration of solutions. Here's how it works:- \( M_1 \): Molarity of the concentrated stock solution.- \( V_1 \): Volume of the stock solution required for dilution.- \( M_2 \): Molarity of the final diluted solution.- \( V_2 \): Volume of the final solution.Using this formula, you can determine how much of the concentrated solution is needed to achieve a particular concentration and volume of the final solution. For example, in the problem, we determine that \( V_1 = 0.323 \mathrm{L} \) of \( 2.00 \mathrm{M} \) HCl is required to prepare \( 1.00 \mathrm{L} \) of \( 0.646 \mathrm{M} \) solution.This formula helps not only in academic settings but also in industries where precise solution preparation is crucial, like pharmaceuticals and chemical manufacturing.